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<title>isNeighbor</title>
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<h1 class="reftitle">isNeighbor</h1>
<h2>Purpose</h2>
<p>Test if a polyhedron touches another polyhedron along a given facet.</p>
<h2>Syntax</h2>
<pre class="synopsis">ts = P.isNeighbor(Q)</pre>
<pre class="synopsis">ts = isNeighbor(P,Q)</pre>
<pre class="synopsis">[ts, iP, iQ] = isNeighbor(P,Q,fP,fQ)</pre>
<h2>Description</h2>
<p></p>
        Return true if the polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor1.png"> shares with the polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor2.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor2.png"> a part of a common facet.
        Both polyhedrons must be in H-representation. If they are not, the irredundant
        H-representation will be computed.
        
        The function tests if the intersection of two polyhedra <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor3.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor3.png"> and <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor4.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor4.png"> in dimension <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor5.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor5.png"> 
        is nonempty and is of dimension <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor6.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor6.png">. If this holds, then the two polyhedra are touching themself
        along one facet. For closer explanation, see the example below.        
	<h2>Input Arguments</h2>
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<td><tt>P</tt></td>
<td>
<p></p>Polyhedron in H-representation<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
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<tr valign="top">
<td><tt>Q</tt></td>
<td>
<p></p>Polyhedron in H-representation<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>fP</tt></td>
<td>
<p></p>Index of a facet to test from polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor7.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor7.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>fQ</tt></td>
<td>
<p></p>Index of a facet to test from polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor8.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor8.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
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<h2>Output Arguments</h2>
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<td><tt>ts</tt></td>
<td>
<p></p>Logical statement if the polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor9.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor9.png"> touches <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor10.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor10.png"> along the facet.<p>
	    		Class: <tt>logical</tt><p>Allowed values:</p><ul>
<li><tt>true</tt></li>
<li><tt>false</tt></li>
</ul></p>
</td>
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<td><tt>iP</tt></td>
<td>
<p></p>Index of a facet from polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor11.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor11.png"> that touches the polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor12.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor12.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
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<td><tt>iQ</tt></td>
<td>
<p></p>Index of a facet from polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor13.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor13.png"> that touches the polyhedron <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor14.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor14.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
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</tbody>
</table>
<h2>Example(s)</h2>
<h3>Example 
				1</h3>Create three neighboring polyhedra <tt>R1</tt>, <tt>R2</tt>, and <tt>R3</tt>.<pre class="programlisting"> R1 = Polyhedron([0 0; 2 0; 0 1; 2 1]); </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> R2 = Polyhedron([1 0; 2 0; 1 -1; 2 -1]); </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> R3 = Polyhedron([2 0; 3 0; 2 -1; 3 -1]); </pre>
<pre class="programlisting"></pre> Plot the polyhedrons to see that they are touching themself.<pre class="programlisting"> plot([R1 R2 R3], 'showindex', true) </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor_img_1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isneighbor_img_1.png" width="60%"></p> Check that polyhedron R1 touches polyhedron R2. <pre class="programlisting"> R1.isNeighbor(R2) </pre>
<pre class="programlisting">
ans =

     1

</pre> Check that the fourth facet of the polyhedron R2 touches the second facet of polyhedron R3.<pre class="programlisting"> [ts, iR2, iR3] = R2.isNeighbor(R3) </pre>
<pre class="programlisting">
ts =

     1


iR2 =

     2


iR3 =

     4

</pre> Actually, the facets of <tt>R2</tt> and <tt>R3</tt> are the same, so these polyhedra have face to face property
        that can be checked using <tt>isAdjacent</tt> method. <pre class="programlisting"> R2.isAdjacent(R3) </pre>
<pre class="programlisting">
ans =

     1

</pre>
<h2>See Also</h2>
<a href="./isadjacent.html">isadjacent</a><p></p>
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<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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